анализ временных рядов

Time-delayed systems, including coupled ones, became popular models of different physical and biological objects. Often One or few variables of such models cannot be directly measured, these variables are called hidden variables. However, reconstruction of models from experimental signals in presence of hidden variables can be very suitable for model verification and indirect measurement.

Purpose. To suggest a new approach to reconstruction of couping architecture and individual parameters of first-order time-delayed oscillators from experimental series of their oscillations.

The methods for the reconstruction of model delay-differential equations for ensembles of coupled time-delay systems from their time series are proposed. The methods efficiency is illustrated using chaotic and periodic time series from chains of diffusively coupled model and experimental time-delay systems for the cases of unidirectional andmutual coupling.

Theoretical background of the wavelet­analysis and a series of applications of the given method are considered including a study of clustering phenomena for synchronous dynamics in structural units if the kidney, tactile information encoding by neurons of the trigeminal complex and detection of information messages from the chaotic carrying signal.

The method is proposed for delay time estimation in time-delay systems from their time series. The method is based on the nearest neighbor method. It can be applied to a wide class of time-delay systems and it is still efficient under very high levels of dynamical and measurement noise.

We propose a new method for analysis of electroencephalograms. It is based on construction of a parameterized stochastic model of the observed process (evolution operator). A certain functional form of the evolution operator is proposed. This form describes deterministic properties of the investigated process, as well as stochastic ones. The parameters of the evolution operator are reconstructed from the experimental data by using the Bayesian approach. New («fast») dynamical variables, which allow for the peculiar features of electroencephalogram, are found.